Going back to the 'factor set' thing I mentioned before, imagine setting up the drought scenario within that framing.
The initial factor cards are:
- Crop Failure: If this card is still in play in two weeks, it converts to the Food Shortage card. Furthermore, this card reduces the degree to which the locals are willing to cooperate with any plans by 1 level.
- Wildfires: While this card is in play, each week 10% of the population will need to evacuate the area or die, and a major building will be destroyed. Fires may also strike at random, preventing any plans that involve construction. Furthermore, this card reduces the degree to which the locals are willing to cooperate with any plans by 1 level.
- Water Shortage: While this card is in play, 10% of the population will die of thirst each week. Furthermore, this card reduces the degree to which the locals are willing to cooperate with any plans by 1 level.
- Heatwave: While this card is in play, any actions taken by PCs or locals incur one level of Exhaustion per hour unless the character is protected from extreme heat. So long as this card is in play, the Wildfires and Water Shortage cards return each week if otherwise temporarily dealt with. Reduces local labor power by 2 levels.
- Rainshadow: Local weather patterns mean that air coming down off of the nearby mountain is dry and hot. Heatwave Factor - if there are at least three Heatwave Factor cards present, the Heatwave card returns each week.
- Summer Weather: It is currently the hot and dry time of year. As long as this persists, this card is a Heatwave Factor
- Pyromancer Enclave: A group of pyromancers are doing large-scale fire magic nearby, amplifying the hot and dry circumstances. This card is a Heatwave Factor
- Vanishing Snowmelt: Permafrost in the nearby mountains has reduced over past years, and snowmelt is not providing enough water for the old riverways to run. This card is a Heatwave Factor.
Other relevant factor cards:
- Food Shortage: While this card is in play, 5% of the population will die of hunger each week. Furthermore, this card reduces the degree to which the locals are willing to cooperate with any plans by 1 level.
- Rampant Disease: If over 100 people die and are not properly buried or cremated, this card appears. Reduces local labor power by 2 levels.
Scenario Goal:
- Remove the Heatwave card.
Then you have resource pools:
- Local cooperativity: 0 is neutral, modified down to -2 by Crop Failure and Water Shortage. Must be positive for any plan involving local participation. Must be 3+ for any plan involving local sacrifices.
- Local labor: 3 baseline, reduced 2 due to Heatwave to 1. Determines the manpower (and therefore speed of completion) for projects involving locals working to help. At 1, you might get a local to guide you around. A small work crew of 10 people could be spared at 2, a large work crew of 100 at 3, etc.
Then, you can have a number of skillful actions that interact with these states. Morale-boosting or diplomatic acts can increase Cooperativity in mechanically specified ways. Sourcing supplies of food or water could temporarily remove those shortages and free people up for larger plans. Building permanent lines of trade or diverting a river could permanently remove shortages. An individual character might not be able to do things like make fire breaks to remove the Wildfires danger (but maybe a high enough level/stat/etc character could?) but if you can hit the minimum local labor rating required you can just have a work crew do it - at 2 it might take a month but at 3 it could be done in 3 days, so it matters a lot as far as how much damage the wildfires will do in the end.
Some actions might convert one card into another. Setting up lines of trade to transport water over might create a card Water Trade - As long as the town has wealth, the Water Shortage card is suppressed. Maybe there's something you can do to redirect a river towards the town, effectively converting the Vanishing Snowmelt card into Flash Flooding. Etc.
Yes, its still going to be the DM adjudicating what sorts of transformations happen. But there's a bit more of a framework saying 'why is this situation happening', 'what does movement through the space of situations look like?', etc. You could make it more quantitative, focusing on general rules for things like local labor that will apply across all scenarios, or you could drop or abstract those elements into a single card like 'Local Panic - as long as there are immediate threats to life and limb, the locals will not lend aid to your plans' or just leave it to narration and table discussion.
5e skills aren't really quite the right skills for this kind of thing though. Honestly, just having lots of examples of big things you can do - organize a trade route; construct a building, a channel, a bridge; determine the causes of a natural phenomenon and how it could be interferred with; etc, would help. With those bigger scope examples, you wouldn't necessarily need to be so detailed with the factor cards and their transformations because it would be implied by the more expansive text. Yes, your character with proficiency in Survival can redirect a river or cause a landslide with a week's labor. Or is it Strength + Architecture? ...